If anyone is interested, I was able to fix my problem.
The problem was the outgoing SMTP port. The app defaults to port 465 but I needed to use port 587. However, the app is flawed in that once you create an account, you cannot edit the server configurations, so I was unable to change the port. I tried deleting and re-adding the account, but the app seems to remember your server config and doesn't let you re-config. So then I tried deleting the app entirely, reinstalling, and that also did not work. It still remembered my settings.
The way I fixed it was by choosing to delete the account "and remote data". Apparently MS keeps your config settings on a remote server. Once I did this type of delete, I was able to re-add the account with port 587 (and I also had to disable SSL), and it now works.
MS really needs to add the ability to modify existing account config settings (among other things).